scholarly journals On the autonomous Nemytskii operator between Sobolev spaces in the critical and supercritical cases: Well-definedness and higher-order chain rule

2022 ◽  
Vol 214 ◽  
pp. 112576
Author(s):  
Florin Isaia
Keyword(s):  
Sobolev Spaces ◽  
Higher Order ◽  
Chain Rule ◽  
Nemytskii Operator

Weighted higher order exponential type inequalities in metric spaces and applications

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Huiju Wang ◽  
Pengcheng Niu
Keyword(s):  
Homogeneous Space ◽  
Lie Groups ◽  
Sobolev Spaces ◽  
Exponential Type ◽  
Metric Spaces ◽  
Type Inequality ◽  
Higher Order ◽  
Geodesic Space ◽  
Stratified Lie Groups ◽  
Weighted Case

AbstractIn this paper, we establish weighted higher order exponential type inequalities in the geodesic space {({X,d,\mu})} by proposing an abstract higher order Poincaré inequality. These are also new in the non-weighted case. As applications, we obtain a weighted Trudinger’s theorem in the geodesic setting and weighted higher order exponential type estimates for functions in Folland–Stein type Sobolev spaces defined on stratified Lie groups. A higher order exponential type inequality in a connected homogeneous space is also given.

scholarly journals Approximation in higher-order Sobolev spaces and Hodge systems

2019 ◽  
Vol 276 (5) ◽  
pp. 1430-1478 ◽  
Author(s):  
Pierre Bousquet ◽  
Emmanuel Russ ◽  
Yi Wang ◽  
Po-Lam Yung
Keyword(s):  
Sobolev Spaces ◽  
Higher Order

scholarly journals Some Opial Dynamic Inequalities Involving Higher Order Derivatives on Time Scales

2012 ◽  
Vol 2012 ◽  
pp. 1-22 ◽  
Author(s):  
Samir H. Saker
Keyword(s):  
Time Scales ◽  
Hölder’S Inequality ◽  
Higher Order ◽  
Chain Rule ◽  
Simple Consequence ◽  
Hölder's Inequality ◽  
Special Cases ◽  
Discrete Inequalities

We will prove some new Opial dynamic inequalities involving higher order derivatives on time scales. The results will be proved by making use of Hölder's inequality, a simple consequence of Keller's chain rule and Taylor monomials on time scales. Some continuous and discrete inequalities will be derived from our results as special cases.

scholarly journals A duality-type method for the obstacle problem

2013 ◽  
Vol 21 (3) ◽  
pp. 181-196 ◽  
Author(s):  
Diana Rodica Merlusca
Keyword(s):  
Sobolev Spaces ◽  
Obstacle Problem ◽  
Optimization Problem ◽  
Quadratic Optimization ◽  
Higher Order ◽  
Type Method ◽  
Quadratic Optimization Problem ◽  
Approximate Problem ◽  
Duality Property ◽  
New Type

Abstract Based on a duality property, we solve the obstacle problem on Sobolev spaces of higher order. We have considered a new type of approximate problem and with the help of the duality we reduce it to a quadratic optimization problem, which can be solved much easier.

scholarly journals How to Recognize Polynomials in Higher Order Sobolev Spaces

2013 ◽  
Vol 112 (2) ◽  
pp. 161 ◽  
Author(s):  
Bogdan Bojarski ◽  
Lizaveta Ihnatsyeva ◽  
JUHA KINNUNEN JUHA KINNUNEN
Keyword(s):  
Sobolev Spaces ◽  
Remainder Term ◽  
Integral Condition ◽  
Higher Order ◽  
Order Case

This paper extends characterizations of Sobolev spaces by Bourgain, Brézis, and Mironescu to the higher order case. As a byproduct, we obtain an integral condition for the Taylor remainder term, which implies that the function is a polynomial. Similar questions are also considered in the context of Whitney jets.

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